Trans-Neptunian binaries as evidence for planetesimal formation by the streaming instability


A critical step toward the emergence of planets in a protoplanetary disk is the accretion of planetesimals, bodies 1–1,000 km in size, from smaller disk constituents. This process is poorly understood, partly because we lack good observational constraints on the complex physical processes that contribute to planetesimal formation1. In the outer Solar System, the best place to look for clues is the Kuiper belt, where icy planetesimals survive to this day. Here we report evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrated clumps of pebbles gravitationally collapse into 100-kilometre-class bodies2. Gravitational collapse has previously been suggested to explain the ubiquity of equal-sized binaries in the Kuiper belt3,4,5. We analyse new hydrodynamical simulations of the streaming instability to determine the model expectations for the spatial orientation of binary orbits. The predicted broad inclination distribution with approximately 80% of prograde binary orbits matches the observations of trans-Neptunian binaries6. The formation models that imply predominantly retrograde binary orbits (for example, ref. 7) can be ruled out. Given its applicability over a wide range of protoplanetary disk conditions8, it is expected that the streaming instability also seeded planetesimal formation elsewhere in the Solar System, and beyond.

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Fig. 1: Three snapshots from our 3D simulation of the SI where the nonlinear particle clumping triggers gravitational collapse into planetesimals.
Fig. 2: The matching properties of model (triangles) and observed (red and blue dots) binary planetesimals.
Fig. 3: The inclination distribution of binary orbits obtained in the SI model (bold solid line) matches observations of trans-Neptunian binaries (bold dashed line).

Data availability

The data that support the plots within this Letter and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The Athena code is available on GitHub ( The PLAN code is available on Zenodo44.


  1. 1.

    Youdin, A. N. & Kenyon, S. J. in Planets, Stars and Stellar Systems Vol. 3 (eds Oswalt, T. D., French, L. M. & Kalas, P.) 1–62 (Springer, 2013).

  2. 2.

    Youdin, A. N. & Goodman, J. Streaming instabilities in protoplanetary disks. Astrophys. J. 620, 459–469 (2005).

    ADS  Article  Google Scholar 

  3. 3.

    Nesvorný, D., Youdin, A. N. & Richardson, D. C. Formation of Kuiper Belt binaries by gravitational collapse. Astron. J. 140, 785–793 (2010).

    ADS  Article  Google Scholar 

  4. 4.

    Noll, K. S., Grundy, W. M., Chiang, E. I., Margot, J.-L. & Kern, S. D. in The Solar System Beyond Neptune (eds Barucci, M. A., Boehnhardt, H., Cruikshank, D. P. & Morbidelli, A.) 345–363 (University of Arizona Press, 2008).

  5. 5.

    Fraser, W. C. et al. All planetesimals born near the Kuiper belt formed as binaries. Nat. Astron. 1, 0088 (2017).

    Article  Google Scholar 

  6. 6.

    Grundy, W. M. et al. Mutual orbit orientations of transneptunian binaries. Icarus (2019).

  7. 7.

    Goldreich, P., Lithwick, Y. & Sari, R. Formation of Kuiper-belt binaries by dynamical friction and three-body encounters. Nature 420, 643–646 (2002).

    ADS  Article  Google Scholar 

  8. 8.

    Yang, C.-C., Johansen, A. & Carrera, D. Concentrating small particles in protoplanetary disks through the streaming instability. Astron. Astrophys. 606, A80 (2017).

    Article  Google Scholar 

  9. 9.

    Johansen, A. et al. Rapid planetesimal formation in turbulent circumstellar disks. Nature 448, 1022–1025 (2007).

    ADS  Article  Google Scholar 

  10. 10.

    Johansen, A., Youdin, A. & Mac Low, M.-M. Particle clumping and planetesimal formation depend strongly on metallicity. Astrophys. J. Lett. 704, 75–79 (2009).

    ADS  Article  Google Scholar 

  11. 11.

    Bai, X.-N. & Stone, J. M. Dynamics of solids in the midplane of protoplanetary disks: implications for planetesimal formation. Astrophys. J. 722, 1437–1459 (2010).

    ADS  Article  Google Scholar 

  12. 12.

    Carrera, D., Gorti, U., Johansen, A. & Davies, M. B. Planetesimal formation by the streaming instability in a photoevaporating disk. Astrophys. J. 839, 16 (2017).

    ADS  Article  Google Scholar 

  13. 13.

    Kenyon, S. J. & Luu, J. X. Accretion in the Early Kuiper Belt. I. Coagulation and velocity evolution. Astron. J. 115, 2136–2160 (1998).

    ADS  Article  Google Scholar 

  14. 14.

    Morbidelli, A., Bottke, W. F., Nesvorný, D. & Levison, H. F. Asteroids were born big. Icarus 204, 558–573 (2009).

    ADS  Article  Google Scholar 

  15. 15.

    Weidenschilling, S. J. Initial sizes of planetesimals and accretion of the asteroids. Icarus 214, 671–684 (2011).

    ADS  Article  Google Scholar 

  16. 16.

    Simon, J. B., Armitage, P. J., Youdin, A. N. & Li, R. Evidence for universality in the initial planetesimal mass function. Astrophys. J. Lett. 847, 12–17 (2017).

    ADS  Article  Google Scholar 

  17. 17.

    Li, R., Youdin, A. N. & Simon, J. B. On the numerical robustness of the streaming instability: particle concentration and gas dynamics in protoplanetary disks. Astrophys. J. 862, 14–29 (2018).

    ADS  Article  Google Scholar 

  18. 18.

    Stone, J. M., Gardiner, T. A., Teuben, P., Hawley, J. F. & Simon, J. B. Athena: a new code for astrophysical MHD. Astrophys. J. Suppl. Ser. 178, 137–177 (2008).

    ADS  Article  Google Scholar 

  19. 19.

    Hayashi, C. Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog. Theor. Phys. Suppl. 70, 35–53 (1981).

    ADS  Article  Google Scholar 

  20. 20.

    Poincaré, H. Mémoires et observations. Sur l’équilibre d’une masse fluide animée d’un mouvement de rotation. Bull. Astron. 2, 109–118 (1885).

    Google Scholar 

  21. 21.

    Benecchi, S. D., Noll, K. S., Stephens, D. C., Grundy, W. M. & Rawlins, J. Optical and infrared colors of transneptunian objects observed with HST. Icarus 213, 693–709 (2011).

    ADS  Article  Google Scholar 

  22. 22.

    Johansen, A. & Lacerda, P. Prograde rotation of protoplanets by accretion of pebbles in a gaseous environment. Mon. Not. R. Astron. Soc. 404, 475–485 (2010).

    ADS  Google Scholar 

  23. 23.

    Gladman, B., Marsden, B. G. & Vanlaerhoven, C. in The Solar System Beyond Neptune (eds. Barucci, M. A., Boehnhardt, H., Cruikshank, D. P. & Morbidelli, A.) 43–57 (University of Arizona Press, 2008).

  24. 24.

    Parker, A. H. & Kavelaars, J. J. Destruction of binary minor planets during Neptune scattering. Astrophys. J. Lett. 722, 204–208 (2010).

    ADS  Article  Google Scholar 

  25. 25.

    Schlichting, H. E. & Sari, R. The ratio of retrograde to prograde orbits: a test for Kuiper Belt binary formation theories. Astrophys. J. 686, 741–747 (2008).

    ADS  Article  Google Scholar 

  26. 26.

    Johansen, A., Mac Low, M.-M., Lacerda, P. & Bizzarro, M. Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion. Sci. Adv. 1, 1500109 (2015).

    ADS  Article  Google Scholar 

  27. 27.

    Bottke, W. F. et al. The fossilized size distribution of the main asteroid belt. Icarus 175, 111–140 (2005).

    ADS  Article  Google Scholar 

  28. 28.

    Petit, J.-M. et al. The absolute magnitude distribution of cold classical Kuiper belt objects. In American Astronomical Society DPS Meeting 48 120.16 (AAS, 2016).

  29. 29.

    Stern, A. et al. Initial results from the New Horizons exploration of 2014 MU69, a small Kuiper belt object. Science 364, eaaw9771 (2019).

    ADS  Article  Google Scholar 

  30. 30.

    Shannon, A. & Dawson, R. Limits on the number of primordial scattered disc objects at Pluto mass and higher from the absence of their dynamical signatures on the present-day trans-Neptunian populations. Mon. Not. R. Astron. Soc. 480, 1870–1882 (2018).

    ADS  Article  Google Scholar 

  31. 31.

    Colella, P. Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87, 171–200 (1990).

    ADS  MathSciNet  Article  Google Scholar 

  32. 32.

    Colella, P. & Woodward, P. R. The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54, 174–201 (1984).

    ADS  Article  Google Scholar 

  33. 33.

    Toro, E. F. Riemann Solvers and Numerical Models for Fluid Dynamics (Springer, 1999).

  34. 34.

    Bai, X.-N. & Stone, J. M. Particle-gas dynamics with Athena: method and convergence. Astrophys. J. Suppl. Ser. 190, 297–310 (2010).

    ADS  Article  Google Scholar 

  35. 35.

    Hockney, R. W. & Eastwood, J. W. Computer Simulation Using Particles (McGraw-Hill, 1981).

  36. 36.

    Youdin, A. & Johansen, A. Protoplanetary disk turbulence driven by the streaming instability: linear evolution and numerical methods. Astrophys. J. 662, 613–626 (2007).

    ADS  Article  Google Scholar 

  37. 37.

    Hawley, J. F., Gammie, C. F. & Balbus, S. A. Local three-dimensional magnetohydrodynamic simulations of accretion disks. Astrophys. J. 440, 742–763 (1995).

    ADS  Article  Google Scholar 

  38. 38.

    Simon, J. B., Armitage, P. J., Li, R. & Youdin, A. N. The mass and size distribution of planetesimals formed by the streaming instability. I. The role of self-gravity. Astrophys. J. 822, 55–72 (2016).

    ADS  Article  Google Scholar 

  39. 39.

    Masset, F. FARGO: a fast eulerian transport algorithm for differentially rotating disks. Astron. Astrophys. Suppl. Ser. 141, 165–173 (2000).

    ADS  Article  Google Scholar 

  40. 40.

    Stone, J. M. & Gardiner, T. A. Implementation of the shearing box approximation in Athena. Astrophys. J. Suppl. Ser. 189, 142–155 (2010).

    ADS  Article  Google Scholar 

  41. 41.

    Koyama, H. & Ostriker, E. C. Pressure relations and vertical equilibrium in the turbulent, multiphase interstellar medium. Astrophys. J. 693, 1346–1359 (2009).

    ADS  Article  Google Scholar 

  42. 42.

    Abod, C. P. et al. The mass and size distribution of planetesimals formed by the streaming instability. II. The effect of the radial gas pressure gradient. Preprint at (2018).

  43. 43.

    Chiang, E. & Youdin, A. N. Forming planetesimals in solar and extrasolar nebulae. Annu. Rev. Earth Planet. Sci. 38, 493–522 (2010).

    ADS  Article  Google Scholar 

  44. 44.

    Li, R. PLAN: PLanetesimal ANalyzer version 0.2, (2018).

  45. 45.

    Eisenstein, D. J. & Hut, P. HOP: a new group-finding algorithm for N-body simulations. Astrophys. J. 498, 137–142 (1998).

    ADS  Article  Google Scholar 

  46. 46.

    Morton, G. M. A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing (International Business Machines, 1966).

  47. 47.

    Barnes, J. & Hut, P. A hierarchical O(N log N) force-calculation algorithm. Nature 324, 446–449 (1986).

    ADS  Article  Google Scholar 

  48. 48.

    Lissauer, J. J. & Kary, D. M. The origin of the systematic component of planetary rotation. I—Planet on a circular orbit. Icarus 94, 126–159 (1991).

    ADS  Article  Google Scholar 

  49. 49.

    Dones, L. & Tremaine, S. On the origin of planetary spins. Icarus 103, 67–92 (1993).

    ADS  Article  Google Scholar 

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The work of D.N. was funded by the NASA Emerging Worlds programme. R.L. acknowledges support from NASA grant NNX16AP53H. A.N.Y. acknowledges support from NASA through grant NNX17AK59G and the NSF through grant 1616929. The funding sources of J.B.S. are NASA grants NNX13AI58G, NNX16AB42G, 80NSSC18K0640 and 80NSSC18K0597. W.M.G.’s contribution was supported in part by NASA Keck PI Data Awards, administered by the NASA Exoplanet Science Institute, and in part by data analysis grants from the Space Telescope Science Institute (STScI), operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under NASA contract NAS 5-26555.

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D.N. suggested a comparison of clump obliquities with binary orbit inclinations and prepared the manuscript for publication. R.L. ran one of the Athena simulations and performed data analyses with PLAN. A.N.Y. developed scaling relations for planetesimal mass estimates. J.B.S. ran two of the Athena simulations. W.M.G. provided the data on trans-Neptunian binaries. All authors contributed to the interpretation of the results and writing of this letter.

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Correspondence to David Nesvorný.

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Peer review information: Nature Astronomy thanks J. J. Kavelaars and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Nesvorný, D., Li, R., Youdin, A.N. et al. Trans-Neptunian binaries as evidence for planetesimal formation by the streaming instability. Nat Astron 3, 808–812 (2019).

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